Finite Group Databasebeta

← #14677351

Subgroups — #14677351

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic, complemented
3C2×#10622591C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622603—24no—
52#10622591—24no—
53#10622571—24no—
54#10622570C418yescomplemented
55C22⋊C4×Dic11—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—41no—
102C2×C22⋊Dic11C2×C414yes—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4C2×C414yescomplemented
120C2×(C2×D11)⋊C4C2×C414yescomplemented
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4C2×C414yescomplemented
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11C2×C414yescomplemented
136C11×#95—22no—
137C11×#95—41no—
138C11×#95—41no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95D414yes—
151C11⋊#95D414yescomplemented
152#14034—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11C22×C412yes—
166C24×C11#4112yes—
167C24×C11#4112yes—
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11C22×C412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11#4112yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C22×Dic11—28no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—44no—
272C22×Dic11—44no—
273C22×Dic11—44no—
274C22×Dic11—44no—
275C22×Dic11—44no—
276C22×Dic11—44no—
277C22×Dic11C22×C412yes—
278C22×Dic11C22×C412yes—
279C22×Dic11C22×C412yes—
280C22×Dic11C2×D412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11#4112yes—
285C22×Dic11#4112yes—
286C22×Dic11#4112yes—
287C22×Dic11#4112yes—
288C22×Dic11#4112yes—
289C11×C4⋊C4—44no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301Dic11⋊C4—28no—
302C4×Dic11—44no—
303C4×Dic11—44no—
304C4×Dic11—44no—
305C4×Dic11—44no—
306C2×#390—111no—
307C2×#388—111no—
308C2×#387—111no—
309C2×#386—111no—
310C2×C4×C22⋊C4—111no—
311#1445—111no—
312#1440—111no—
313#1439D1111yescharacteristic, complemented
314#1438—111no—
315#1437—111no—
316#1437—111no—
317#1437—111no—
318#1434—111no—
319C22⋊#95—111no—
320C4×#95—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11#11714yes—
356C23×C11C23×C411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C22⋊D11—416no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—416no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11C4×D414yes—
497C2×Dic11C4×D414yes—
498C2×Dic11#12414yes—
499C23×D4—111no—
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4C2×D1111yescharacteristic
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4C2×D1111yescharacteristic
512C22×C22⋊C4C2×D1111yescharacteristic
513C22×C22⋊C4C2×D1111yescharacteristic
514C22×C42—111no—
515C22×C42—111no—
516C22×C42—111no—
517C22×C42—111no—
518#390—118no—
519#388—224no—
520#387—224no—
521#386—224no—
522C4×C22⋊C4—224no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11—24no—
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11C2×#11711yescharacteristic
555C22×C11C2×C4×D411yescharacteristic
556C22×C11C2×C4×D411yescharacteristic
557C22×C11C4×#4111yescharacteristic
558C22×C11C4×#4111yescharacteristic
559C22×C11#51811yescharacteristic
560C22×C11#51811yescharacteristic
561C22×C11#52511yescharacteristic
562C22×C11#52511yescharacteristic
563C22×C11C2×#12411yescharacteristic
564C22×C11#52911yescharacteristic
565C22×C11#52911yescharacteristic
566C22×C11#52911yescharacteristic
567C22×C11#52911yescharacteristic
568C22×C11#53211yescharacteristic
569C22×C11#53811yescharacteristic
570C22×C11#53811yescharacteristic
571C22×C11#54011yescharacteristic
572C22×C11#54011yescharacteristic
573C22×C11D4211yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#54611yescharacteristic
576C22×C11#54611yescharacteristic
577C22×C11#54611yescharacteristic
578C22×C11#55011yescharacteristic
579C22×C11#55011yescharacteristic
580C22×C11#55111yescharacteristic
581C22×C11#55111yescharacteristic
582C22×C11#55111yescharacteristic
583C22×C11#55111yescharacteristic
584C22×C11#55311yescharacteristic
585C22×C11#55311yescharacteristic
586C22×C11#55311yescharacteristic
587C22×C11#55311yescharacteristic
588C22×C11#55911yescharacteristic
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—81no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C2×D11—81no—
602C2×D11—81no—
603C2×D11—81no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—81no—
610Dic11—24no—
611Dic11—24no—
612Dic11—24no—
613Dic11—42no—
614Dic11—42no—
615Dic11—42no—
616Dic11—81no—
617C25—111no—
618C25C22×D1111yescharacteristic
619C22×D4—114no—
620C22×D4—222no—
621C22×D4—222no—
622C22×D4—222no—
623C22×D4—222no—
624C22×D4—441no—
625C22×D4—441no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—222no—
634C23×C4—222no—
635C23×C4—222no—
636C23×C4—222no—
637C23×C4—222no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—114no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4C4×D1114yes—
685C2×C42—114no—
686C2×C42—222no—
687C2×C42—222no—
688C2×C42—222no—
689C2×C42—222no—
690C2×C42—222no—
691C2×C42—222no—
692C2×C42—441no—
693C2×C42—441no—
694C2×C42—441no—
695C2×C42—441no—
696C2×C42—441no—
697#95—22no—
698#95—41no—
699#95—41no—
700#95—114no—
701#95—114no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—222no—
711#95—441no—
712#95—441no—
713C2×C11—44no—
714C2×C11#229011yescharacteristic
715C2×C11C4×#12411yescharacteristic
716C2×C11#233311yescharacteristic
717C2×C11#234211yescharacteristic
718C2×C11#235311yescharacteristic
719C2×C11#236411yescharacteristic
720C2×C11#236611yescharacteristic
721C2×C11#246411yescharacteristic
722C2×C11#246711yescharacteristic
723C2×C11#247111yescharacteristic
724C2×C11#247211yescharacteristic
725C2×C11#249011yescharacteristic
726C2×C11#251611yescharacteristic
727C2×C11#255411yescharacteristic
728C2×C11#259511yescharacteristic
729D11—82no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—112no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24C2×C4×D1112yes—
758C24#434112yes—
759C24#434312yes—
760C24C23×D1111yescharacteristic
761C2×D4—228no—
762C2×D4—228no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—228no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4—444no—
859C22×C4—444no—
860C22×C4—444no—
861C22×C4C2×C4×D1112yes—
862C22×C4C2×C4×D1112yes—
863C22×C4D4×D1112yes—
864C22×C4D4×D1112yes—
865C22×C4#434112yes—
866C4⋊C4—44no—
867C4⋊C4—228no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—228no—
872C22⋊C4—228no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C42—444no—
880C42—444no—
881C42—444no—
882C42—444no—
883C11#1403411yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23#6694514yes—
954C23C22×C4×D1111yescharacteristic
955C23C2×D4×D1111yescharacteristic
956C23C2×D4×D1111yescharacteristic
957C23C2×#434111yescharacteristic
958C23C2×#434111yescharacteristic
959C23#6703711yescharacteristic
960C23#6703711yescharacteristic
961C23#6703711yescharacteristic
962C23C2×#434311yescharacteristic
963C23#41×D1111yescharacteristic
964C23#41×D1111yescharacteristic
965C23#41×D1111yescharacteristic
966C23#41×D1111yescharacteristic
967C23#41×D1111yescharacteristic
968C23#6704211yescharacteristic
969D4—4416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—114no—
1013C2×C4—114no—
1014C2×C4—114no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—4416no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—881no—
1085C22—881no—
1086C22—881no—
1087C22—881no—
1088C22—881no—
1089C22—881no—
1090C22—881no—
1091C22—881no—
1092C22#1062301711yescharacteristic
1093C22C2×#6694511yescharacteristic
1094C22#1062305311yescharacteristic
1095C22C4×#434111yescharacteristic
1096C22C4×D4×D1111yescharacteristic
1097C22C4×D4×D1111yescharacteristic
1098C22#1062307611yescharacteristic
1099C22#1062311711yescharacteristic
1100C22#1062312111yescharacteristic
1101C22#1062312211yescharacteristic
1102C22#1062312711yescharacteristic
1103C22#1062313011yescharacteristic
1104C22#1062313011yescharacteristic
1105C22#1062313211yescharacteristic
1106C22#1062313211yescharacteristic
1107C22#1062314111yescharacteristic
1108C22#1062314611yescharacteristic
1109C22#1062314811yescharacteristic
1110C22#1062315511yescharacteristic
1111C22#1062315811yescharacteristic
1112C22#1062316111yescharacteristic
1113C22#1062316811yescharacteristic
1114C22#1062316811yescharacteristic
1115C22#1062316811yescharacteristic
1116C22#1062318011yescharacteristic
1117C22#1062318011yescharacteristic
1118C22#1062318911yescharacteristic
1119C22#1062319211yescharacteristic
1120C22#1062319511yescharacteristic
1121C22D11×#12411yescharacteristic
1122C22#1062320711yescharacteristic
1123C22#1062320911yescharacteristic
1124C22#1062323711yescharacteristic
1125C22#1062324011yescharacteristic
1126C22#1062325011yescharacteristic
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—224no—
1134C4—224no—
1135C4—224no—
1136C4—442no—
1137C4—442no—
1138C4—442no—
1139C4—881no—
1140C2—44no—
1141C2—882no—
1142C2#1307105211yescharacteristic
1143C2#1307115711yescharacteristic
1144C2#1307137511yescharacteristic
1145C2#1307146311yescharacteristic
1146C2#1307155811yescharacteristic
1147C2#1307166011yescharacteristic
1148C2#1307167911yescharacteristic
1149C2#1307261511yescharacteristic
1150C2#1307266011yescharacteristic
1151C2#1307273011yescharacteristic
1152C2#1307274511yescharacteristic
1153C2#1307296111yescharacteristic
1154C2#1307324311yescharacteristic
1155C2#1307366911yescharacteristic
1156C2#1307414011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14034
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622603C2semidirect
3. C2×#10622591C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066882C2semidirect
7. #13066864C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. #13066852C2semidirect
12. #13066840C2semidirect
13. #13066838C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1439C2semidirect
54. #10622570C4semidirect
119. C2×(C2×D11)⋊C4C2×C4semidirect
120. C2×(C2×D11)⋊C4C2×C4semidirect
123. C2×Dic11⋊C4C2×C4semidirect
135. C2×C4×Dic11C2×C4semidirect
151. C11⋊#95D4semidirect
313. #1439D11semidirect
883. C11#14034semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225702
C2×#106226032
C2×#106225912
C2×#106225712
C2×C22⋊C4×Dic112
#130668822
#130668642
#130668552
#130668532
#130668522
#130668402
#130668382
#95×Dic112
C11×#14392
#1403411